what is the root of 9386 through division method according to cbse NCERT
Answers
Answer:
there you go = 96.881370758263
Step-by-step explanation:
Step 1:
Divide the number (9386) by 2 to get the first guess for the square root .
First guess = 9386/2 = 4693.
Step 2:
Divide 9386 by the previous result. d = 9386/4693 = 2.
Average this value (d) with that of step 1: (2 + 4693)/2 = 2347.5 (new guess).
Error = new guess - previous value = 4693 - 2347.5 = 2345.5.
2345.5 > 0.001. As error > accuracy, we repeat this step again.
Step 3:
Divide 9386 by the previous result. d = 9386/2347.5 = 3.9982960596.
Average this value (d) with that of step 2: (3.9982960596 + 2347.5)/2 = 1175.7491480298 (new guess).
Error = new guess - previous value = 2347.5 - 1175.7491480298 = 1171.7508519702.
1171.7508519702 > 0.001. As error > accuracy, we repeat this step again.
Step 4:
Divide 9386 by the previous result. d = 9386/1175.7491480298 = 7.9829953657.
Average this value (d) with that of step 3: (7.9829953657 + 1175.7491480298)/2 = 591.8660716977 (new guess).
Error = new guess - previous value = 1175.7491480298 - 591.8660716977 = 583.8830763321.
583.8830763321 > 0.001. As error > accuracy, we repeat this step again.
Step 5:
Divide 9386 by the previous result. d = 9386/591.8660716977 = 15.8583173607.
Average this value (d) with that of step 4: (15.8583173607 + 591.8660716977)/2 = 303.8621945292 (new guess).
Error = new guess - previous value = 591.8660716977 - 303.8621945292 = 288.0038771685.
288.0038771685 > 0.001. As error > accuracy, we repeat this step again.
Step 6:
Divide 9386 by the previous result. d = 9386/303.8621945292 = 30.8890022154.
Average this value (d) with that of step 5: (30.8890022154 + 303.8621945292)/2 = 167.3755983723 (new guess).
Error = new guess - previous value = 303.8621945292 - 167.3755983723 = 136.4865961569.
136.4865961569 > 0.001. As error > accuracy, we repeat this step again.
Step 7:
Divide 9386 by the previous result. d = 9386/167.3755983723 = 56.0774694237.
Average this value (d) with that of step 6: (56.0774694237 + 167.3755983723)/2 = 111.726533898 (new guess).
Error = new guess - previous value = 167.3755983723 - 111.726533898 = 55.6490644743.
55.6490644743 > 0.001. As error > accuracy, we repeat this step again.
Step 8:
Divide 9386 by the previous result. d = 9386/111.726533898 = 84.0086922286.
Average this value (d) with that of step 7: (84.0086922286 + 111.726533898)/2 = 97.8676130633 (new guess).
Error = new guess - previous value = 111.726533898 - 97.8676130633 = 13.8589208347.
13.8589208347 > 0.001. As error > accuracy, we repeat this step again.
Step 9:
Divide 9386 by the previous result. d = 9386/97.8676130633 = 95.905067123.
Average this value (d) with that of step 8: (95.905067123 + 97.8676130633)/2 = 96.8863400932 (new guess).
Error = new guess - previous value = 97.8676130633 - 96.8863400932 = 0.9812729701.
0.9812729701 > 0.001. As error > accuracy, we repeat this step again.
Step 10:
Divide 9386 by the previous result. d = 9386/96.8863400932 = 96.8764016782.
Average this value (d) with that of step 9: (96.8764016782 + 96.8863400932)/2 = 96.8813708857 (new guess).
Error = new guess - previous value = 96.8863400932 - 96.8813708857 = 0.0049692075.
0.0049692075 > 0.001. As error > accuracy, we repeat this step again.
Step 11:
Divide 9386 by the previous result. d = 9386/96.8813708857 = 96.8813706308.
Average this value (d) with that of step 10: (96.8813706308 + 96.8813708857)/2 = 96.8813707583 (new guess).
Error = new guess - previous value = 96.8813708857 - 96.8813707583 = 1.274e-7.
1.274e-7 <= 0.001. As error <= accuracy, we stop the iterations and use 96.8813707583 as the square root.